In various areas such as information processing and information communication, as one of the means for analyzing the characteristics of numerical data, a method for detecting the periodicity that exists in numerical data is required. The “periodicity” present in numerical data means a state in which a repeat of a certain numerical pattern is found in a numerical data series.
FIG. 17 is a diagram illustrating an example of a repeat of numerical pattern. Numerical data to be processed includes, for example, data indicative of a periodical time interval, and data indicative of a periodical position interval such as distance and length, as shown in FIG. 17.
Generally, when detecting periodicity present in numerical data, the detection may be achieved without using any information about periodicity present in the numerical data. A periodic component of which the periodic pattern is composed may include randomness or small fluctuations as shown in FIG. 17. Here, the “periodic component” is an element of the numerical data of which a repeating pattern with periodicity is composed.
An example of a device or a technique for detecting such periodicity of the numerical data is disclosed in patent literature 1 and non-patent literature 1. In patent literature 1 discloses a periodicity detection device which defines an n dimensional phase space to continuous n numerical data, and detects the periodic pattern by extracting a feature point corresponding to the periodic component in the space.
The periodicity detection device described in patent literature 1 records an appearance frequency of the numerical data in a coordinate position in the n dimensional phase space determined by the numerical data, and extracts a coordinate position whose appearance frequency is high as a feature point indicating the periodic component. When the periodicity of a specific repeating pattern exists in the numerical data, with respect to the periodic component of which the periodic pattern is composed, a pattern, which starts from a feature point corresponding to a first periodic component in the n dimensional phase space and ends at a feature point corresponding to the last periodic component via one or a plurality of coordinate positions extracted as the feature point, is detected.
At this time, the feature point corresponding to the first periodic component and the feature point corresponding to the last periodic component are located at the same position in the n dimensional phase space, and a trajectory of the feature points forms a closed loop. When the first feature point and the last feature point are located at the same position in the closed loop, this means that the same numerical data elements appear. Therefore, this result may be considered as the periodicity. The periodicity detection device described in patent literature 1 detects the periodic pattern in the numerical data by utilizing the above-mentioned characteristic.
In a periodicity detection method described in non-patent literature 1, a real number axis is evenly divided according to a predetermined value with respect to numerical data represented by a real number, and each section is defined as a slot. After that, it is determined whether or not the numerical data to be processed exists in each slot and a flag is given to the slot to which it is determined that the numerical data exists. The periodic component is identified by searching for the interval of the slot to which the flag is given and the periodic pattern is detected.
Specifically, in the periodicity detection method described in non-patent literature 1, the search is performed for all the possible slot interval in all the slots. For example, the search is performed for one slot interval, two slot intervals, . . . , and n slot intervals. When there are N slots in the real number axis, the number of candidates for the slot interval is equal to N/2 and the search is performed for all the candidates.